Asymptotic Properties of Residual Based Tests for Cointegration

Peter Phillips and Sam Ouliaris

Econometrica, 1990, vol. 58, issue 1, 165-93

Abstract: This paper develops an asymptotic theory for residual based tests for cointegration. Attention is given to the augmented Dickey-Fuller (ADF) test and the Z(subscript "alpha") and Z(subscript "t") unit root tests. Two new tests are also introduced. The tests are shown to be asymptotically similar, and simple representations of their limiting distributions are given and asymptotic critical values are tabulated. The ADF and Z(subscript "t") tests are asymptotically equivalent. Power properties of the test are also studied. The tests are consistent if suitably constructed, but the ADF and Z(subscript "t") tests have slower rates of divergence under cointegration than the other tests. Copyright 1990 by The Econometric Society.

Date: 1990
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Related works:
Working Paper: Asymptotic Properties of Residual Based Tests for Cointegration (1988)
Software Item: POTEST: RATS procedure to perform Phillips-Ouliaris-Hansen test for Cointegration
Software Item: POTESTRESIDS: RATS procedure to perform Phillips-Ouliaris-Hansen test for Cointegration on 1st stage residuals
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